The weak gravity conjecture applied for the aligned natural inflation indicates that generically there can be a modulation of the inflaton potential, with a period determined by sub-Planckian axion scale. We study the oscillations in the primordial power spectrum induced by such modulation, and discuss the resulting observational constraints on the model. (C) 2016 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license.